11317
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
The Arithmetic-Geometric Mean Inequality (I)
The arithmetic-geometric mean inequality:
, for
.
The figure shows that
, therefore
.
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
THINGS TO TRY
Rotate and Zoom in 3D
Gamepad Controls
SNAPSHOTS
DETAILS
Reference: D. Schattschneider, "Proof without Words: The Arithmetic Mean-Geometric Mean Inequality,"
Mathematics Magazine
,
59
(1), 1986 p. 11.
RELATED LINKS
Arithmetic Mean
(
Wolfram
MathWorld
)
Geometric Mean
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
The Arithmetic-Geometric Mean Inequality (I)
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheArithmeticGeometricMeanInequalityI/
Contributed by:
Soledad Mª Sáez Martínez
and
Félix Martínez de la Rosa
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
The Arithmetic-Geometric Mean Inequality (III)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Arithmetic-Geometric Mean Inequality (II)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
The Arithmetic-Logarithmic-Geometric Mean Inequality
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Hadwiger-Finsler Inequality
Jay Warendorff
Solving Linear Inequalities
Izidor Hafner
Sum of the Alternating Harmonic Series (I)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Representations of Trigonometric and Hyperbolic Functions in Terms of Sector Areas
S. M. Blinder
The Erdös-Mordell Inequality
Jay Warendorff
A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius
Jay Warendorff
Napier's Inequality (I)
Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
Related Topics
Algebra
Area
Inequalities
Plane Geometry
Theorem Proving
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+